Kubica announced earlier this year that he would be leaving the outfit at the end of the season amid a difficult comeback in which he has been stuck at the back of the grid.
Latifi has worked as a test driver for the Grove-squad this year, while also handling Formula 2 duties. He has taken part in six FP1 sessions with Williams in 2019.
"I am thrilled to be stepping up as race driver for 2020," Latifi said. "I have thoroughly enjoyed working with the team this year, supporting them with the development of the car, and assisting wherever I can trackside and at the factory.
"I look forward to the journey ahead with the team, and I am excited to make my Formula 1 debut at the Australian Grand Prix in 2020.”
Latifi is in a battle for second place in the F2 championship, as rival Nyck de Vries wrapped up the championship last time out in Sochi.
The 24-year-old will be partnered by George Russell next year, who himself is bringing his maiden season in F1 to an end this weekend in Abu Dhabi.
Deputy team principal of Williams Claire Williams added: “I am delighted to announce that Nicholas will be stepping up to the role of Race Driver to partner George in 2020.
"All of us at Williams have been immensely impressed at what he has achieved this year in FIA Formula 2, along with his commitment to the team, and the work that he has put in behind the scenes.
"Nicholas has become an established and well-respected member of Williams, and we look forward to him stepping up into this new role, as we look to fight our way back to the midfield.”
Bahrain International Circuit - Winter testing